Related papers: Partition Eisenstein series and semi-modular forms
Given the L-series of a half-integral weight cusp form, we construct a cohomology class with coefficients in a finite dimensional vector space in a way that parallels the Eichler cohomology in the integral weight case. We also define a lift…
A cubic partition is an integer partition wherein the even parts can appear in two colors. In this paper, we introduce the notion of generalized cubic partitions and prove a number of new congruences akin to the classical Ramanujan-type. We…
We describe "quasi canonical modules" for modular invariant rings $R$ of finite group actions on factorial Gorenstein domains. From this we derive a general "quasi Gorenstein criterion" in terms of certain 1-cocycles. This generalizes a…
We establish sufficient conditions, involving Rankin--Cohen (RC) brackets, under which certain combinations of meromorphic quasi-modular forms and their derivatives yield meromorphic modular forms. To achieve this, we adopt an algebraic…
Let $G_{2n}$ be the Eisenstein series of weight $2n$ for the full modular group $\Gamma=SL_2(\ZZ)$. It is well-known that the space $M_{2k}$ of modular forms of weight $2k$ on $\Gamma$ has a basis $\{G_{4}^\alpha G_{6}^\beta\ |\…
Numerical semigroups are cofinite additive submonoids of the natural numbers. In 2011, Keith and Nath illustrated an injection from numerical semigroups to integer partitions. We explore this connection between partitions and numerical…
Recently, Andrews introduced separable integer partition classes and analyzed some well-known theorems. In this paper, we investigate partitions with parts separated by parity introduced by Andrews with the aid of separable integer…
For each prime $\ell$, let $|\cdot|_\ell$ be an extension to $\bar \Q$ of the usual $\ell$-adic absolute value on $\Q$. Suppose $g(z) = \sum_{n=0}^\infty c(n)q^n \in M_{k+\half}(N)$ is an eigenform whose Fourier coefficients are algebraic…
In this short note, inspired by much recent activity centered around attempts to formulate various correspondences between the classification of affine SU(k) WZW modular-invariant partition functions and that of discrete finite subgroups of…
We establish analogues in the context of group actions or group representations of some classical problems and results in additive combinatorics of groups. We also study the notion of left invariant submodular function defined on power sets…
This note reveals a mysterious link between the partition function of certain dimer models on 2-dimensional tori and the $L$-function of their spectral curves. It also relates the partition function in certain families of dimer models to…
A classical method for partition generating functions is developed into a tool with wide applications. New expansions of well-known theorems are derived, and new results for partitions with n copies of n are presented.
We define a reflective numerical semigroup of genus $g$ as a numerical semigroup that has a certain reflective symmetry when viewed within $\mathbb{Z}$ as an array with $g$ columns. Equivalently, a reflective numerical semigroup has one gap…
In this monograph, we study in detail a special class of $GL_2$-real analytic Eisenstein series.
We will give the graded ring of Siegel modular forms of degree two with respect to a non-split symplectic group explicitly.
In this paper we consider certain classes of generalized double Eisenstein series by simple differential calculations of trigonometric functions. In particular, we give four new transformation formula for some double Eisenstein series. We…
A Chevalley type integral basis for the ortho-symplectic Lie superalgebra is constructed. The simple modules of the ortho-symplectic supergroup over an algebraically closed field of prime characteristic not equal to 2 are classified, where…
In this article using the theory of Eisenstein series, we give rise to the complete evaluation of two Gauss hypergeometric functions. Moreover we evaluate the modulus of each of these functions and the values of the functions in terms of…
For any length category, we establish a set of rules (necessary and sufficient) that ensure a partial order on the isomorphism classes of simple objects such that the category is equivalent to the category of finite dimensional…
We show that a semi-classical quantum field theory comes with a versal family with the property that the corresponding partition function generates all path integrals and satisfies a system of 2nd order differential equations determined by…